A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement

Authors Yannis Coutouly, Emmanuel Godard

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Yannis Coutouly
  • Laboratoire d'Informatique et des Systèmes - Université Aix-Marseille, France
  • CNRS, Marseille, France
Emmanuel Godard
  • Laboratoire d'Informatique et des Systèmes - Université Aix-Marseille, France
  • CNRS, Marseille, France

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Yannis Coutouly and Emmanuel Godard. A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The Iterated Immediate Snapshot model (IIS) is a central model in the message adversary setting. We consider general message adversaries whose executions are arbitrary subsets of the executions of the IIS message adversary. We present a complete and explicit characterization and lower bounds for solving set-agreement for general sub-IIS message adversaries. In order to have this characterization, we introduce a new topological approach for such general adversaries, closely associating executions to geometric simplicial complexes. This way, it is possible to define and explicitly construct a topology directly on the considered sets of executions. We believe this topology by geometrization to be of independent interest and a good candidate to investigate distributed computability in general sub-IIS message adversaries, as this could provide both simpler and more powerful ways of using topology for distributed computability.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • topological methods
  • geometric simplicial complex
  • set-agreement


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